FT 

MEADE 

4GV 
1423 
Copy 1 

. . .RLOR PROBLEMS 

OR 

MENTAL MATHEMATICAL 
MAGIC 

BY 

Preston Langley Hickey 





The John J. and Hanna M. McManus 
and Morris N. and Chesley V. Young 
Collection 


PARLOR PROBLEMS 


OR 

MENTAL MATHEMATICAL 
MAGIC 


PRESTON LANGLEY HICKEY 


AUTHOR OF 

“Practical Drawing Room Club and Stage Patter,” etc. 



PRINTED BY 

Augsburg Publishing House 

MINNEAPOLIS, MINN. 


COPYRIGHT NOTICE. 


The entire contents of this booklet are fully protected by 
copyright under the laws of the United States of America, 
including the translation into foreign languages. (This 
includes also the Scandinavian.) Permission must be ob- 
tained from the author before any of the contents of this 
book either as a whole or individually may be reprinted. 


(Copyright, 1920, by the Author.) 


Tke JOHN j 
Morris 



Gift— Oct. 12, 1955 


DEDICATION 


To my four friends Collins Pentz, 
Raymond Erickson, Ira Olson and 
Jack Makiesky, I take great pleasure 
in dedicating this small offering to 
the already vast world of literature 
devoted to the art of entertaining. 










































•4--GcV 


1423 






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Contents 


page 


Introduction 7 

Chapter One 9 

Chapter Two 11 

Chapter Three 24 

Afterword 28 


-• 


< 






INTRODUCTION 


Nearly every person of normal faculties at- 
tends parties and social gatherings. As a rule 
some sort of a little entertainment is given. Some 
one will sing, speak a piece or play some instru- 
ment. While they are very fine, and it takes long 
practise to become accomplished in these lines, 
people are constantly on the look out for some- 
thing new. 

Parlor Problems, is therefore offered to the 
public as something new. Become an efficient en- 
tertainer in something outside of the beaten path 
and you materially increase your popularity. 

Master the few effects herein contained, and 
you are master of the situation as an original en- 
tertainer presenting something entirely different 
from the accomplishments of tho general public. 

Besides being amusing, puzzling and astonish- 
ing, the problems of which the book is made up, 
will give you an insight into an angle of mathe- 
matics, that, perhaps, you never before knew 
existed. 

The little problems of lightning addition and 
multiplication herein contained, are something 
that no grade, high, business school or college 


8 


Parlor Problems 


professor in the country make a practise of teach- 
ing. Very few of them know these secrets and if 
they do they reserve them for themselves. 

With a little serious study and concentration 
you will soon master the following problems, 
which will not only prove of satisfaction to your- 
self, but will amuse your friends and increase 
your own popularity. 

The Author. 

“Harmon Place” 

Minneapolis, Minnesota. 

Feb. 1920 


CHAPTER ONE 
The Basic Number 

It is especially important that the student of 
this little treatise should read thoroughly and 
very carefully this first chapter, “The Basic 
Number”, if he is to free himself of a lot of un- 
necessary confusion as to the Why and How the 
following problems are brought to their final and 
correct solutions. 

The whole thing in a nut shell, so to speak, is 
that there really is no Why and How. Prac- 
tically speaking, the problems just work them- 
selves out, and with the only exception of care- 
less or intentional mistakes, they are always cor- 
rect. (By intentional mistakes, I mean those 
who perhaps would endeavor to spoil your trick 
or belittle you. The world is full of these kind 
of people.) 

However, there is just one little thing that 
while it will not in any manner simplify the work- 
ing principles (a simplified method is not neces- 
sary) of the forthcoming, it is well for the stu- 
dent to know. 

Every type of arithmetic known is based on 


10 


Parlor Problems 


what is termed the basic figure or number. That 
is the figure nine (9). 

The figure 9 is constantly being employed by 
large corporations, where a great deal of mathe- 
matical work is done, especially banks, to 
straighten out accounts wherein mistakes have 
occurred. 

Give an expert accountant a report, that con- 
tains some kind of a miscalculation, and with the 
figure 9 he will eventually ferret out the mistake 
regardless of how glaring or complex it may be. 

With but one exception, the tricks and rapid 
calculations contained in this little booklet, are 
accomplished with the use of the figure 9 in some 
manner or other, either directly or indirectly. 

Perhaps there are some who have thought 
deeply enough to explain why this is, but as I 
have heard so many such explanations, no two of 
which have been the same, I place little faith in 
them. 

This is a good point to remember, though, in 
case some one should spring a mathematical 
problem of the type that are in this book on you, 
go to work with your basic figure 9 and the 
chances are ten to one that you will discover 
their secret. 


CHAPTER TWO 
Lightning Addition 

The following experiment though so simple as 
to be almost laughable can be worked innumer- 
able times without fear of detection, unless 
viewed by someone who perhaps has read its 
secret. 

Request one of your spectators to give you 
three numbers, each containing four figures. We 
will assume, as an illustration, that they are the 
following; 2956-5840-6753. Put these down in 
regular addition order, and explain that you will 
add a couple of numbers of your own and in- 
stantly tell them what the sum is. You then 
write down two four figure numbers, 4159 and 
3246. Quick as a flash, without so much as glanc- 
ing at the numbers, you write down the total which 
will be 22954. 

Observe carefully the five figures which I 
have set down in regular addition form, so that 
I may explain more comprehensively the method 
by which this clever little experiment is accom- 
plished. 


12 


Parlor Problems 


Spectator’s - 2 9 5 6 - figure 

” - 5 8 4 0 - ” 

” -6 7 5 3 - ” 

Your - 4 1 5 9 - ” 

” , 3 2 4 6 - ” 


Total - 2 2, 9 5 4 

The first three figures from the top are the 
ones given you by the spectator. The last two 
are your own. I have selected the first figure 
from which to form my answer, therefore the 
secret lies in the first figure of the spectator’s and 
the two I put down myself. 

Leaving the first number your spectator gave 
you, for a moment, I would call your attention 
to the last four. The second and third are the 
other two you were instructed to write down; 
while the fourth and fifth are your own. Take 
a pencil and draw lines connecting the second and 
fourth numbers, and also lines connecting the third 
and fifth. Take the numbers individually and 
you will find that the first figure of the second 
number and the first figure of the fourth number 
added together equal nine. 

The second figures of these numbers added 
also equal 9, and so on. With the third and 
fifth numbers, the individual figures of the third 
added with the individual figures of the fifth, the 
result wiil be the same. 

To procure the answer, take the first number, 


Parlor Problems 


13 


2956, subtract 2 from the last figure which is 6 
and place it in front of the first number which is 
2. This gives you 22,954 which is the correct 
answer. It never fails. 

The reason that you subtract 2 from the last 
figure of the first number is because you have 
two sets of figures that total nine. If you had 
only one set you would merely subtract 1. (A 
problem with only 1 set of nines, would naturally 
be worked with three numbers instead of five.) 
On the other hand, if you had three sets of nines 
you would subtract three from the last number 
and place it in front of the first. 

Any one of the three figures that the specta- 
tors give you can be used to get your answer. 
You will merely have to match up the other two 
into sets of nines. 

In some instances you might be working the 
problem with five number figures instead of four. 
It is possible that the figure you have selected for 
your answer will end in a double ought (0). Take 
for instance 35,900. 

As it is impossible to subtract anything from 
0 you would have to take the number 3-2-1 or 
whatever it is, according to the number of sets 
of nines you have lined up, from the first num- 
ber to the left of the oughts, including them. If 
you are to subtract the number 2, you will have 
to take 2 away from 900. Thus your answer de- 
rived from 35,900 will be 235,898. 


14 


Parlor Problems 


Additional surprise and astonishment can be 
produced, by writing down what your answer is 
to be after the first figure has been called by your 
spectator. The reader will readily see how easily 
this can be accomplished. All that is necessary 
is to figure before hand how many sets of nines 
you are going to have and then subtract this 
amount from the first figure, as has been ex- 
plained. 

Lightning Multiplication 

On a sheet of paper write down the two larg- 
est single numbers possible which will, of course, 
be 99. Then request one of your spectators to 
give you any two numbers smaller than the ones 
you have written down, and you will show them 
a feat of rapid multiplication. As an easy example 
we will assume that they give you 75. Place the 
75 under the 99, and immediately write out your 
answer which will be 7425. 

This is purely a problem of elimination. Using 
the above figures as an example, read carefully 
the following. Although the answer gained will 
be that of the two figures multiplied, the trick is 
accomplished by a process of subtraction. 

Place your 99 down with the 75 under it. 

99 

75 


Then subtract your 75 from 100 which will 


Parlor Problems 1 5 

leave 25. The 25 will be the first two figures of 
your product. 

99 

75 


25 

For the final step of the problem subtract 1 
from the 75 which leaves 74. This is placed as 
the first two figures of the product, thus giving 
you the same total as though you had multiplied 
them. 

99 

75 


7425 

If the figures are 99 and 65, the process is the 
same. Sixty five from 100 leaves 35. Subtract 
1 from 65 and you have 64. Thus your final 
product of 99 multiplied by 65 will be 6435. 

The only quick work required is to be able to 
instantly subtract the figure that your spectator 
gives you from 100 in your mind. 

Cross Out Number Trick 

In the following the performer explains to his 
audience that he is going to accomplish a feat 
by “mental concentration.” This of course will 
be laughed at by the “wise” spectator, because 
there is no mental concentration about it, but as 


16 


Parlor Problems 


the trick is too easily done to be caught at it, why 
not add more mystery to the effect by stringing 
your audience a little. It does no harm to say 
the least, and if anyone is “chump” enough to 
take you seriously, that is their fault not yours. 

Have some one set down any four numbers in 
a row. For example, 2-6-8 7. Then request 
them to add the numbers together and set down 
their total. The above four figures added to- 
gether will make a total of 23. After this has 
been done have them go back and cross out any 
one of the four figures that they feel inclined to. 
Take for instance 6 is crossed out. Make dash 
thru figure 6. Then have them write down the 
remaining three figures so as to form a solid fig- 
ure; which will be 287. When this has been ac- 
complished, ask them to subtract the added total, 
which was 23 from the remaining three figures. 
Twenty-three from 287 leaves a remainder of 
264. Then have them take the numbers of the 
remainder individually and add them together. 
2-6-4 added will make 12. 

During this entire operation your back has 
been turned so as not to see What figures have 
been written down, and which one was scratched 
out. Ask your spectator to tell you what his final 
answer is and you will tell him what figure is 
marked out. He complies with your request and 
instantly you tell him which one it was that was 
crossed. In this instance, it was the figure 6. 


Parlor Problems 


17 


The following is the manner in which this 
should look when completely set down on paper. 

2-6-8-7—23 

287 

23 


264—12 

The method of determining what figure has 
been crossed out is exceedingly simple. 

The entire secret is based on what the next 
multiple of 9 above the final answer is. In the 
illustration herein contained 12 is the final an- 
swer. The next multiple of 9 above 12 is 18. 
You then subtract your final answer from the 
next multiple of 9, and the difference will be the 
figure that has been crossed out. Twelve sub- 
tracted from 18 leaves 6. Six was the figure 
crossed out. If the first answer should be 8, sub- 
tract 8 from the next multiple of 9, which would 
naturally enough be 9. The remainder would 
be 1. One would be the number that had been 
crossed out. 

There is only one final answer that might stick 
you and that is a multiple itself. If the answer 
is a 9 or 18 there are two possible numerals that 
they might have crossed out. It is either a 9 or 
a 0. I have been caught this way several times, 
and have always answered that they crossed out 
an 0. It has always been correct. The chances 


18 


Parlor Problems 


are that in 99 out of every 100 instances where- 
in the final answer is either 9 or 18 that the num- 
eral crossed out is a 0. 

Even though you should make an error in 
this case, the trick is so good that an occasional 
mistake is excusable. 

Multiplication Extraordinary 

Place before your spectators a sheet of paper 
on which you have written the figures 1 to 9, ex- 
cluding the 8. That is, in this manner 1-2-3-4-5- 
6-7-9T Ask one of them to select any one of the 
numbers. Some one selects number 6. Tell 
them to take the above row of figures as a whole 
number, multiply it by 54, and the answer will 
be 666,666,666. 

You will note that every figure in the answer 
is the same as was selected. To prove this for 
your own benefit, I will work it out here. 

12345679 

54 


49382716 

61728395 

666,666,666 

This is accomplished by mentally multiplying 
the number they select by the highest figure in 


Parlor Problems 


19 


the number, which is 9, and then multiplying the 
entire number by that result. 

If the figure selected was four (4), you would 
multiply the entire number by 4 times nine (9) 
which is 36. If it was 5 the multiplier would 
be 5 times 9 which is 45, and so on. 

Forty-Five From Forty-Five 

Write down the figure 45 and ask your spec- 
tators if they can take 45 from 45 and still have 
45 left. Explain to them that they are allowed 
to split the number up into as many smaller num- 
bers as they desire to, but the figures of the final 
difference added together must make 45. They 
will, in all probability, have to give it up. Here 
is the way to do it. 

9-8-7-6-5-4-3-2-1—45 
1-2-3-4-5-6-7-8-9 — 45 


8-6-4- 1-9-7-5-3-2 — 45 

The minuend and subtrahend are made up of 
exactly the same figures only the minuend is re- 
versed. The difference of the two also contains 
exactly the same figures. The individual figures 
of each added together will give you 45. Note 
the above. 


20 


Parlor Problems 


The Mental Number Trick 

Request some one to think of a number but 
caution him to keep it to himself and not tell you. 
Then have him double it. When this is done ask 
him to add, say — 10. Then tell him to take 
half of it. When he has also done this, tell him 
to take away the number he thought of in the 
first place, and quick as a flash you tell him what 
he has left. In this case it will be five (5). 

Regardless of what the spectator thinks of, his 
final answer will always be just half of the num- 
ber you tell him to add. 

As an illustration. Suppose he thinks of 25. 
Tell him to double his number which will be fifty 
. (50). Then ask him to add 10. This will make 
a total answer of 60. Have him take half of it 
which leaves 30. Then request him to take 
away the number he thought of in the first place, 
which was 25, and his answer will be 5. This 
being just half the amount you told him to add. 

If you tell him to add 6 his answer will be 3. 
If 14 was the number you gave him 7 would be 
the result. This can also be worked out in a frac- 
tion. That is if you request him to add 7, he 
would have 3*4 left after the final deduction 
had been made. 

A Salary Increase 

The following is not a trick, and is not sup- 
posed to mystify or create astonishment. It is 


Parlor Problems 


21 


merely a little mathematical calculation from 
which much amusement can be derived. 

A young Jewish man worked in the clothing 
store of another Jewish personage. He was re- 
ceiving a modest salary for his work, but he felt 
that he was not getting his right dues. So one 
morning he approached his employer with a re- 
quest for more wages. The employer thought 
for a moment, then motioned the young man to 
a chair. When the young man had seated him- 
self, the employer picked up a pencil and began. 

“Isaac, in an ordinary year there are 365 
days. Am I not right?” 

The other nodded. 

“Well, this being leap year there are 366 
days,” and he wrote this down. “Now Isaac, you 
work a third of your time, play a third of your 
time, and sleep the other third. Isn’t that so?” 

The other agreed wondering what all this had 
to do with his request for higher pay. 

“Well then, you only work one third of your 
time, don’t you?” 

“Yes.” 

“One third of 366 days is 122 days, that is the 
time you spend in actual work. Now there are 4 
legal holidays every year, Christmas, New Years, 
Fourth of July and Thanksgiving. On these days 
you do not work, do you?” 

“No.” 

“Very well, we will take 4 more days for holi* 


22 


Parlor Problems 


days away from the 122 days of actual work 
you do, and that leaves 118 days. Alright, Jew- 
ish people never work on Saturday. There are 
52 Saturdays in every year, and taking 52 from 
118 leaves a remainder of 66 days. Our store 
is never open Sundays Isaac, and as there are 
also 52 Sundays in a year, we will subtract that 
amount from 66, which leaves just 14 days. 

“Now Isaac, my boy, I am pretty liberal with 
you. Don’t I give you two weeks vacation every 
summer?” 

“Yes,” replied the other. 

“Good. Now you subtract the two weeks, 
which is fourteen days from the 14 days you have 
left and you have nothing. No Isaac my boy, 
you aren’t working at all according to this, and 
don’t need a raise. Go back to your work and 
be content.” 

And Isaac went. 


* * * 

This little mathematical monologue, for that 
is what it is, will always prove popular wher- 
ever you show it. The conversation I have given 
above is just for an outline. You should take a 
piece of paper and as you are telling the story 
keep jotting the figures down at the proper time 
for their introduction. When complete, the dia- 
gram should look as follows, without the explan- 
atory writing. 


Parlor Problems 


23 


365 days in ordinary years 
Wk one third of time. 3)366( ” ” Leap 


122=days of actual labor 
4=National holidays 


118 

52=Saturdays, store closed 


66 

52=Sundays 


14 

14=Two weeks’ vacation 


Total 00 


CHAPTER THREE 
The Cannibals And White Men 

If we should attempt to estimate the number 
of puzzles that there are in existence at the pres- 
ent time I dare say that they would run into the 
tens of thousands. Some are excellent. Others 
are mediocre; while still others, the greatest ma- 
jority of all, are worthless. 

Among the first class is one, so good, and so 
almost impossible to work unless you are on to 
it, that I am setting it down here for your ap- 
proval. It is so catchy, that even after you are 
once familiar with the right moves, you will find 
yourself stumped, when it comes to accomplishing 
it, until you have a thorough working picture of 
the layout in your mind. You can even offer a 
dollar*as a prize to anyone who can successfully 
accomplish it under the rules. The offering of 
the money makes it harder still for the victim, 
as his mind is divided between the puzzle and the 
expectancy of victory, where if there were no in- 
ducement his whole attention would be centered 
on the one thing. 

On a sheet of paper draw two straight parallel 


Parlor Problems 


25 


lines about three inches apart to represent a river. 
Lay three matches and three toothpicks on one 
“shore.” See figure. 


White Men 

w 

> 


Cannibals 

P< 


X 




X Represents cannibal who can paddle. 


Explain to your spectators that the three 
matches represent white men, and the three tooth- 
picks represent cannibals. Also inform them that 
the whole party are desirous of getting across 
the river, but that owing to the smallness of the 
canoe, only two persons can go at a time. All 
three white men can paddle, but only one canni- 
bal knows how. (It is advisable to place a pen- 
cil mark on the match or toothpick that represents 
the cannibal who can paddle). One cannibal can 



26 


Parlor Problems 


be left with two or all of the white men, and one 
white man and one cannibal may be left together, 
but owing to the extremely vicious nature of the 
cannibals, one white man cannot be left with two 
cannibals, or two white men with three canni- 
bals, because the aforementioned vicious natures 
of these individuals would assert itself, and they 
would forthwith proceed to kill and eat the 
white men. In other words, the number of can- 
nibals on either shore must not be in excess of 
the number of whites. 

Here is a mistake that is often made. They 
will begin by having the cannibal that can paddle 
take a cannibal across, and then coming back and 
taking a white man across. This is incorrect, be- 
cause when he gets the white man over, there 
will be two canibals to the one white man. Your 
spectator will, in all probability, make the reply 
that he had intended bringing the cannibal right 
back with the canoe, but that doesn’t count. The 
fact remains that there are two of them there 
with the one white man. 

As soon as they have tired themselves out and 
have distorted their minds in the attempt, you do 
it for them. Read the following carefully. It 
is best to have the material before you, and make 
each move as you read it, until you have a thor- 
ough mental picture of each step. 

1st move. The cannibal that can paddle takes 
one of the other cannibals over and comes back. 


Parlor Problems 


27 


2nd move. He then takes the other cannibal 
across and returns. This leaves the three white 
men and the cannibal that can paddle on one side, 
and two cannibals on the other side of the river. 

3rd move. Two white men then go over. 

4th move. A white man and a cannibal come 
back. 

5th and 6th moves. The same white man 
then takes the cannibal that can paddle over, and 
brings the other cannibal back. 

This leaves the canoe, two white men and the 
two cannibals that can’t paddle on this side of the 
river, and one white man and the cannibal that 
can paddle on the other side. 

7th move. The two remaining white men go 
over, leaving the two cannibals on this side. 

8th move. The cannibal that can paddle then 
makes two trips bringing one of his fellow men 
over each time. 

Study over the above, and read it several times 
carefully and you will quickly become acquainted 
with the moves. 

Much amusement is often caused by offering 
a prize to the one who can do the stunt. In most 
cases the spectator will give up after a few trials 
with a remark such as this : “Why shouldn’t you 
offer us a prize? — the thing can’t be done.” 
Whereupon you prove to him that it can be done 
and very easily at that. 


AFTERWORD 

Once more I pause, and lay down my pen. 
My present task, the writing of Parlor Problems 
is complete. Short as is the little volume, my 
work has been very pleasant. I cannot but feel 
that in these few pages I have set before the read- 
ing public some new principles in the art of en- 
tertaining, that may be of benefit to them. If so 
I shall be satisfied. If not, my effort has been 
in vain. 

To my many friends both personal and other- 
wise who so graciously received my former book- 
lets, I extend my heartfelt appreciation, with the 
hope that this also will be given a like recep- 
tion. 

Therefore, I, like the late Angelo K. Louis 
(Professor Hoffman), bid you all not good bye 
but Au Revoir for the present. 

Fraternally yours, 
Preston Langley Hickey. 


Jewels of Magic 


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